Let X1, X2,..., Xn be independent exponential random variables with mean ið. For example, E(X1) = 0, E(X2) = 20, etc. Suppose an estimate of of 0 is ô = E ). a. Find the distribution of n. b. Find Elê-11.

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Let X1, X2,..., Xn be independent exponential random variables with mean i. For example, E(X1) = 0, E(X2) = 20,
etc. Suppose an estimate of of 0 is 0 =
E).
a. Find the distribution of 0.
b. Find E[Ô-1].
c. Find the MSE of cô-1 as an estimator of 0-1, and find c that minimizes that MSE.
Transcribed Image Text:Let X1, X2,..., Xn be independent exponential random variables with mean i. For example, E(X1) = 0, E(X2) = 20, etc. Suppose an estimate of of 0 is 0 = E). a. Find the distribution of 0. b. Find E[Ô-1]. c. Find the MSE of cô-1 as an estimator of 0-1, and find c that minimizes that MSE.
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